Spherically symmetric inhomogeneous model with Chaplygin gas

Abstract

We investigate the late time acceleration with a Chaplygin type ofgas in spherically symmetric inhomogeneous model. At the earlyphase we get Einstien-de Sitter type of solution generalised toinhomogeneous spacetime. But at late stage of the evolution oursolutions admit the accelerating nature of the universe. For alarge scale factor our model behaves like a ΛCDM model.We calculate the deceleration parameter for this anisotropicmodel, which, unlike its homogeneous counterpart, shows that theflip is not synchronous occurring early at the outershells. This is in line with other physical processes in anyinhomogeneous models. Depending upon initial conditions oursolution also gives bouncing universe. In the absence ofinhomogeneity our solution reduces to wellknown solutions inhomogeneous case. We have also calculated the effectivedeceleration parameter in terms of Hubble parameter. The wholesituation is later discussed with the help of wellknownRaychaudhury equation and the results are compared with theprevious case. This work is an extension of our recentcommunication where an attempt was made to see if the presence ofextra dimensions and/or inhomogeneity can trigger an inflation ina matter dominated Lemaître Tolman Bondi model.